By analogy with the definition for sheaves, we define the slope of a polarised algebraic variety and of each of its subschemes. This gives a notion of slope stability, which we show is a necessary condition for K-stability. We also give the modifications needed to get a necessary condition for asymptotic Chow stability. We then give various calculations of slope and concrete examples. These examples have been chosen to be of interest to the conjectured correspondence between K-stability and the existence of K¨ahler metrics of constant scalar curvature. In particular we get new examples of polarised manifolds that do not admit such metrics.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:406242 |
| Date | January 2006 |
| Creators | Ross, Julius |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/1250 |
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